what is the point slope form of an equation with the slope of 3/5 that passes through the point (10,-2)

Answers

Answer 1

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 10}}\quad ,&{{ -2}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{3}{5} \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-(-2)=\cfrac{3}{5}(x-10)\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y+2=\cfrac{3}{5}(x-10)[/tex]

Related Questions

Which set or sets does the number 15 belong to?

Answers

It belongs to rational,whole,integer,real.

Hope this helped :)

A fountain on a lake sprays water in a parabolic arch modeled by the equation y = -0.3x2 + 3x. A beam of light modeled by the equation -2x + 5.5y = 19.5 passes through the fountain to create a rainbow effect. If the beam cuts the water spray at points A and B, such that point B is at a higher level than point A, what distance from the ground level is point A?

Answers

check the picture below, so, what is from the A coordinates, what's the y-coordinate then.

well, we can get that off either equation, if we just know A coordinates, so let's see what "x" is at those A and B points.

[tex]\bf \begin{cases} y=-0.3x^2+3x\\ ----------\\ -2x+5.5y=19.5\\\\ y=\cfrac{19.5+2x}{5.5} \end{cases}\implies -0.3x^2+3x=\cfrac{19.5+2x}{5.5} \\\\\\ -1.65x^2+16.5x=19.5+2x\implies 0=1.65x^2-14.5x+19.5 \\\\\\ \textit{using the quadratic formula}\quad x=\cfrac{14.5\pm\sqrt{210.25-4(1.65)(19.5)}}{2(1.65)} \\\\\\ x\approx \begin{cases} 7.13\\ 1.66 \end{cases}\textit{ so those are A and B, who is who?, dunno, let's check}[/tex]

[tex]\bf y=-0.3x^2+3x\qquad x=7.13\qquad y=-0.3(7.13)^2+3(7.13) \\\\\\ y\approx 6.14\\\\ -------------------------------\\\\ y=-0.3x^2+3x\qquad x=1.66\qquad y=-0.3(1.66)^2+3(1.66) \\\\\\ y\approx 4.15[/tex]

so, as you can see, clearly 6.14 is higher, and thus is B.

thus A is 4.15, so the y-coordinate for point A is 4.15, and that's the distance from the beam hitting the fountain at A, to the ground.

Average maintenance costs are $1.50 per machine-hour at an activity level of 8,000 machine-hours and $1.20 per machine-hour at an activity level of 13,000 machine-hours. assuming that this activity is within the relevant range, total expected maintenance cost for a budgeted activity level of 10,000 machine-hours would be closest to:

Answers

Assume that maintenance costs per machine may be modeled by the linear relation
C = a + bx
where
x = machine hours
a, b are constants.

When x=8,000 hours, C=$1.50, therefore
a + 8000b = 1.5 (1)

When x=13,000 hours, C=$1.20, therefore
a + 13000b = 1.2 (2)

Subtract (2) from (1).
a + 8000b - (a + 13000b) = 1.5 - 1.2
-5000b = 0.3
b = -6 x 10⁻⁵
From (1), obtain
a = 1.5 - 8000*(-6 x 10⁻⁵) = 1.98

Therefore
C = 1.98 - 6x10⁻⁵ x

When machine hours is x=10,000, obtain
C = 1.98 - 6x10⁻⁵ * 10000
= 1.38

Answer: $1.38

Jack and Andrea want to create a right triangle together using values of x and y and the polynomial identity to generate Pythagorean triples. If Andrea picks a value of x = 2, and the hypotenuse of the resulting right triangle is 5, what natural number value of y did Jack pick? y = 1 y = 2 y = 3 y = 4

Answers

A right triangle can be considered as a special type because the relationship of its sides can be described using the hypotenuse formula:

c^2 = a^2 + b^2

c^2 = x^2 + y^2

where,

c is the hypotenuse of the triangle and is the side opposite to the 90° angle

while a and b are the sides adjacent to the 90° angle

In the problem statement, we are given that one of the side has a measure of 2 = x, while the hypotenuse is 5 = c, therefore calculating for y:

y^2 = c^2 – x^2

y^2 = 5^2 – 2^2

y^2 = 21

y = 4.58

The natural number is the number before the decimal. Therefore the answer is:

y = 4

Answer:

it is now y=4, i swear!! I put this, and it was wrong!!!

Step-by-step explanation:

how do you write an interger whose absolute value is greater than itself.

Answers

Integers include negative numbers as well as positive numbers and zero.

An example of a solution to your question is -2. Its absolute value is 2, which is more than -2.

All negative integers are valid solutions, though.

A telephone survey uses a random digit dialing machine to call subjects. the random digit dialing machine is expected to reach a live person 15% of the time. in eight attempts, what is the probability of achieving exactly two successful calls?

Answers

P([tex]r[/tex] successes in [tex]n[/tex] trials) = ⁿ[tex] C_{r} [/tex]×[tex] [P(Success)^{r}] [/tex]×[tex] [P(failure)]^{n-r} [/tex]

We have
[tex]n=8[/tex]
[tex]r=2[/tex]
[tex]P(Success)=0.15[/tex]
[tex]P(Failure)=0.85[/tex]

Substitute these values into the formula, we have
P( 2 success in 8 trials) = ⁸C₂ × (0.15)² × (0.85)⁶
P( 2 success in 8 trials) = 0.2376.... ≈ 0.24 = 24%

Final answer:

The probability of achieving exactly two successful calls in eight attempts in a telephone survey using a random digit dialing machine is approximately 0.324 or 32.4%.

Explanation:

To calculate the probability of achieving exactly two successful calls in eight attempts in a telephone survey using a random digit dialing machine, we can use the binomial distribution formula. The formula is:

P(x) = (nCx) * (p^x) * ((1-p)^(n-x))

Where:

P(x) is the probability of getting exactly x successful callsn is the total number of attemptsx is the number of successful callsp is the probability of reaching a live person

Plugging in the values from the question, we have:

P(2) = (8C2) * (0.15^2) * ((1-0.15)^(8-2)) = 28 * 0.0225 * 0.411771 = 0.3239965

Therefore, the probability of achieving exactly two successful calls in eight attempts is approximately 0.324 or 32.4%.

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A single fair die is tossed. Find the probability of rolling a number greater than 4.

Answers

There are two numbers greater than four out of six total numbers so:

P(>4)=2/6

P(>4)=1/3

Final answer:

The probability of rolling a number greater than 4 with a single fair die is 1/3 or approximately 0.33. This is calculated as the number of desired outcomes (a roll of 5 or 6) divided by the total possible outcomes (1, 2, 3, 4, 5, or 6). The actual results of a short series of rolls may vary, but over time the results should average out to this probability.

Explanation:

The question is asking to calculate the probability of rolling a die and getting a number greater than 4. In a fair six-sided die, the possible outcomes of a single toss are 1, 2, 3, 4, 5, or 6, making the total possible outcomes 6. The outcomes greater than 4 are 5 and 6, which gives us 2 desired outcomes.

Remember, probability is calculated as the number of desired outcomes over the number of total possible outcomes. So in this case, the probability is 2 (the number of outcomes greater than 4) divided by 6 (the total number of outcomes when rolling a die) which gives a probability of 1/3 or approximately 0.33.

This suggests that if you throw the single fair die repeatedly over time, about one third of the results would show a number greater than 4. It's essential to remember this is a theoretical probability, and actual short-term results may vary, but they should correspond to this probability in the long run per the law of large numbers.

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Emily has 300 books. If Frank were to double the number of books that he now owns, he would still have fewer than Emily has.

Answers

2F<E, Emily has 300 books

3F<300 divide both sides by 3

F<100

Frank has less than 100 books.

A map has a scale of 1 in. 4 mi. You measure 3 inches between your house and the movie theatre. How many miles is it from your house to the Movie Theatre

Answers

Hi!

1in:4m
3in:xm

3/1 = 3
4 x 3 = 12

1in:4m
3in:12m

The answer is 12

Hope this helps! :)

Answer: x = 12

Step-by-step explanation:

1/3 = 4/x

1x = 12

X = 12

In how many ways can 5 starting positions on a basketball team be filled with 8 men who can play any of the positions?

Answers

8 men, 5 positions

so multiply 8*7*6 =336

divide by 3*2 =6

336/6 =56

56 different ways

Choose the polynomial that is written in standard form. 2x3y2 + 4x4y + 8x7 −3x4y2 + 4x4y5 + 10x2 6xy2 + 4x3y8 + 9x2 −2x5y3 + 4x2y2 + x2

Answers

The first thing that should be considered is alphabetical precedence.
If a term has x in it, it should be considered before y.
Then sort by powers. For example, x^3 should go before x^2.
Finally sort by coefficient if the variables and their powers are the same.
A is incorrect because 8x^7 should go before all else.
B is incorrect because 4x^4 should go before -3x^4.
C is incorrect because the order should be 4x^3, then 9x^2, then 6x
D is correct.

It is D because of the order of the exponents

DE is parallel to XY. What is the value of X?

Answers

DE is parallel to XY
x = 85 (alternate interior angles)
answer is A. 85

Since two opposite angles (vertical) about the intersection of two lines must equal to each other:

x=85°

Tatiana wants to give friendship bracelets to her 32 classmates. She has 5 bracelets now. She can buy more bracelets in packages of 4. If p is the number of packages Tatiana needs to buy to have at least 32 bracelets, the inequality representing the problem is: 4p+5≥32 What is the minimum number of packages Tatiana needs to buy?

Answers

7 packages would equal 28 bracelets, then add the 5 she already has and you get 33 total bracelets.

7 packages is the answer

Let

p--------> the number of packages Tatiana needs to buy

we know that

[tex] 4p+5 \geq 32\\ 4p \geq (32-5)\\ 4p \geq 27\\\\ p \geq \frac{27}{4} \\ \\ p \geq 6.75 [/tex]

therefore

the minimum number of packages does Tatiana needs to buy is [tex] 7 [/tex]

let's check

[tex] 7*4+5=33 [/tex] bracelets

[tex] 33 \geq 32 [/tex] ------> is ok

the answer is

the minimum number of packages is [tex] 7 [/tex]

what is the unit rate

Answers

A unit rate tells the rate in lowest terms or the amount of one it has a denominator of 1

The ratio compares two quantities (in this case blue and white parts).
A unit rate (or unit ratio) describes how many units of the first type of quantity corresponds to one unit of the second type of quantity. In our case the first type of quantity is blue parts and the second is white parts, so we should find how many blue parts correspond to one white part.
The ratio is: 5/4
We will obtain the unit ratio if we divide each number with 4 in order to get 1 - as a second quantity.
So, (5/4)/(4/4)= (5/4)/1
The unit ratio is:
(5/4)/1.

A box contains 5 plain pencils and 7 pens. A second box contains 3 color pencils and 3 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected?

Answers

Multiply the two desired probabilities to find the answer.

5/12 is the probability for the plain pencil since there are 5 pencils out of 12 total items.

1/2 is the probability for the colored pencil since there are 3 colored pencils out of 6 total items. 3/6 simplifies to 1/2.

5/12*1/2= 5/24

Final answer: 5/24

a cell phone company offers two different monthly plans.plan a charges $41 for unlimited cell phone minutes plus $0.10 per text message.Plan b charges $31 for unlimited cell phone minutes plus $0.15 per text message.How many text messages must a customer send in order for the cost of plan a to be equal to cost of plan b?

Answers

41+0.10x = 31+0.15x

10 +0.10x=0.15x

10=0.05x

x=10/.05

x= 200 text messages

check 200*0.10 = 20 +41 =61

200*0.15 = 30+31 = 61

they equal each other so number of texts is 200

What are the zeros of f(x)=4x^3-13x^2-37x+10

Answers

In this question there are 3 points of intersection on the x-axis. Of which are: (5,0), (1/4,0), and (-2,0). Hope this is right!

Given p(a)=0.40, p(b)=0.50. if a and b are independent, what is the value of p(a intersection b)?

Answers

Final answer:

The value of P(A intersection B) is 0.20.

Explanation:

Given that events A and B are independent, the probability of their intersection can be found by multiplying their individual probabilities. So, P(A ∩ B) = P(A) * P(B). From the given information, P(A) = 0.40 and P(B) = 0.50. Therefore, P(A ∩ B) = 0.40 * 0.50 = 0.20.

Of 13 possible books, you plan to take 6 with you on vacation. How many different collections of 6 books can you take?

Answers

Taking into account the definition of combination, you can take 1716 different collections of 6 books.

Combination

Combinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in which the order in which the elements are chosen is not taken into account and repetition is not possible.

The combination is calculated by:

[tex]C=\frac{m!}{n!(m-n)!}[/tex]

The term "n!" is called the "factorial of n" and is the multiplication of all numbers from "n" to 1.

Collections of 6 books that you can take

In this case it is possible to apply a combination, not all the elements enter, the order in which the books are chosen does not matter, and they are not repeated.

Being m= 13 and n=6, the combination is calculated by:

[tex]C=\frac{13!}{6!(13-6)!}[/tex]

Solving:

[tex]C=\frac{13!}{6!7!}[/tex]

C= 1716

Finally, you can take 1716 different collections of 6 books.

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what is the 31st term of the sequence below?
-108, -90, -72, -54, ...

Answers

Answer:

432

Step-by-step explanation:

The form for finding the nth term of an arithmetic sequence is a(n) = b +(n-1)d, where a is the function of the nth term, b is the first number in the sequence, n is the nth term, and d is the common difference. Plugging in what we know we get:

a(31) = -108 + 30 x 18

multiply

a(31) = -108 + 540

add

a(31) = 432

PLEASE MARK BRAINLIEST

Which of the following are true statements about any regular polygon? Check all that apply.

A. All of its angles measure 90.
B. It is a quadrilateral.
C. It is a closed figure.
D. It is a hexagon.
E. All of its angles have equal measures.
F. Its sides are congruent line segments.

Answers

Answer:

Statement C, E and F are true.

Step-by-step explanation:

We have to find the true statements about a regular polygon.

Regular Polygon

A regular polygon is a polygon that is equiangular that is all angles are equal in measure and equilateral that is all sides have the same length.

A) False

This is not a necessity that all angles measure 90 degrees.

B) False

It may or may not be a a quadrilateral.

C) True

All regular polygons are closed figure.

D) False

All regular polygons are not hexagon but hexagon is a polynomial.

E) True

All the angles of a regular polygon are equal.

F) True

Since all the sides of a regular polygon are equal, thus, its sides are congruent line segments.

How do i Divide z4 by z-3

Answers

Synthetic division:

3 | 1 0 0 0 0
... | . 3 9 27 81
- - - - - - - - - - - - - - - -
... | 1 3 9 27 81

which translates to

[tex]\dfrac{z^4}{z-3}=z^3+3z^2+9z+27+\dfrac{81}{z-3}[/tex]

What is the answer to this problme

Answers

w= 4 and x =-2 so____ -2 - 4 which equals -6

w= 4

x=-2

-2-4=-6

the answer is -6

an architect designs a rectangular flower garden such that the width is exactly two thirds of the length if 320 ft of the antique picket fencing are to be used to enclose the garden find the dimensions of the garden

Answers

check the picture below.

what's the width? well, w = (2/3)l.

The dimensions of the garden where 320 ft of the antique picket fencing are to be used to enclose the garden are 96 feet and 64 feet.

Given that:

A garden is in rectangular shape.

The length of the antique picket fencing used to enclose the garden is 320 feet.

The perimeter defines the enclosing length.

So, the perimeter is 320 feet.

Let P = 320.

Let l represent the length and w represents the width of the garden.

The width is exactly two-thirds of the length.

So, [tex]w=\frac{2}{3} l[/tex].

The perimeter of the garden is:

P = 2(l + w)

= 2 (l + [tex]\frac{2}{3} l[/tex])

= [tex]\frac{10}{3} l[/tex]

So, substitute P = 320.

[tex]\frac{10}{3} l=320[/tex]

Simplifying,

l = 96 feet

So, w = 64 feet

Hence, the dimensions are 96 feet and 64 feet.

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The population of a town is modeled by the equation P = 16,581e0.02t where P represents the population t years after 2000. According to the model, what will the population of the town be in 2020?

Answers

2020 is 20 years after 2000, so put 20 where t is in the equation and evaluate.

P = 16,581e^(0.02·20) = 16,581e^0.4

P ≈ 24,736

The model predicts the population in 2020 will be about 24,736.

Kim uses decals to decorate 5 cars and 2 motorbikes. She uses 2/3 of the decals on the cars and 2/5 of the remaining on the motorbikes. She has 6 decals left. How many decals does Kim use on each car?

Answers

She uesed 1/3 * 2/5 of the total decal the second time, which is 2/15. So she used 2/15 + 2/3 = 12/15 of the decal. Which means what's left is 3/15 of the initial number, since its 6, the total number is 30. Which means she used 20 in the car, 4 in each, and 4 on the motorcycle, 2 in each.

the sum of two numbers is 8 and their difference is 2. find the numbers

Answers

5 and 3. 5+3=8 and 5-3=2

The volume of 10,000 drops of a liquid is 1 fluid ounce.
What is the volume of 10
drops?

Answers

1/100th of a fluid ounce because to get 10,000 to 10 you divide by 100 so you would divide 1 by 100 to get 1/100th of a fluid ounce.

44^4 = 22^4 * ? find the missing factor in exponential form. How would you solve this?

Answers

[tex]\bf 44^4=22^4\cdot x\implies (2\cdot 22)^4=22^4x\implies (2^4\cdot 22^4)=22^4x \\\\\\ \cfrac{2^4\cdot \underline{22^4}}{\underline{22^4}}=x\implies 2^4\implies 16=x[/tex]

Answer:

Step-by-step explanation:

Which of the following are solutions to the equation below? (4x - 1)2 = 11

Answers

(4x - 1)2 = 11
(4x - 1) = 22
4x - 1 = 22
4x = 23
x = 5.75

Answer:

X = - sqrt 12 / 4

X = sqrt 11 + 1 / 4

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